Iterative Algorithms for Set Stabilization of Probabilistic Boolean Control Networks and Applications in State-Based Games

IF 8.7 1区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

IEEE Transactions on Systems Man Cybernetics-Systems Pub Date : 2025-07-08 DOI:10.1109/TSMC.2025.3580175

Wen Liu;Jun-e Feng;Renato De Leone;Shihua Fu;Jianwei Xia

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引用次数: 0

Abstract

A probabilistic Boolean control network (PBCN) is a binary discrete-time system that utilizes probability values. An important application of PBCN is in gene regulatory network (GRN), providing a more flexible model, and lay a foundation for the study of gene interactions in complex environments. In this research, the set stabilization with probability 1 of PBCNs is investigated. Utilizing semi-tensor product (STP) of matrices, an iterative algorithm for calculating the largest control invariant subset of PBCNs is established and a necessary and sufficient condition for set stabilization with probability 1 is provided. Moreover, we design an algorithm for the stabilization controller to achieve stabilization of the system in the shortest time. As an application, the results of PBCNs are used to solve the stabilization problems at recurrent state equilibriums (RSEs) of state-based games. Examples are given to verify the feasibility of the proposed method and results.

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概率布尔控制网络集镇定的迭代算法及其在状态博弈中的应用

概率布尔控制网络（PBCN）是一种利用概率值的二元离散系统。PBCN的一个重要应用是在基因调控网络（GRN）中，提供了更灵活的模型，为复杂环境下基因相互作用的研究奠定了基础。本文研究了概率为1的PBCNs集镇定问题。利用矩阵的半张量积（STP），建立了pbcn最大控制不变子集的迭代算法，并给出了集稳定的充分必要条件。此外，我们还设计了一种镇定控制器算法，使系统在最短的时间内实现镇定。作为一种应用，PBCNs的结果被用于解决基于状态的博弈的循环状态均衡（rse）的镇定问题。算例验证了所提方法和结果的可行性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Systems Man Cybernetics-Systems AUTOMATION & CONTROL SYSTEMS-COMPUTER SCIENCE, CYBERNETICS

CiteScore

18.50

自引率

11.50%

发文量

812

审稿时长

6 months

期刊介绍： The IEEE Transactions on Systems, Man, and Cybernetics: Systems encompasses the fields of systems engineering, covering issue formulation, analysis, and modeling throughout the systems engineering lifecycle phases. It addresses decision-making, issue interpretation, systems management, processes, and various methods such as optimization, modeling, and simulation in the development and deployment of large systems.